Question 1 |

The following differential equation has

3(\frac{d^{2}y}{dt^{2}})+4(\frac{dy}{dt})^{3}+y^{2}+2=x

3(\frac{d^{2}y}{dt^{2}})+4(\frac{dy}{dt})^{3}+y^{2}+2=x

degree = 2, order = 1 | |

degree = 3, order = 2 | |

degree = 4, order = 3 | |

degree = 2, order = 3 |

Question 1 Explanation:

Order is highest derivative term. Degree is power
of highest derivative term.

Question 2 |

Choose the function f (t); -\infty \lt t \lt \infty for which a Fourier series cannot be defined.

3sin(25t) | |

4cos(20t+3)+2sin(10t) | |

exp(-|t|)sin(25t) | |

1 |

Question 2 Explanation:

All other functions are either periodic or constant
function.

Question 3 |

A fair dice is rolled twice. The probability that an odd number will follow an
even number is

1/2 | |

1/6 | |

1/3 | |

1/4 |

Question 3 Explanation:

\begin{aligned} P_{0}=\frac{3}{6}=\frac{1}{2} \\ P_{e}=\frac{3}{6}=\frac{1}{2} \end{aligned}

since both events are independent of each other.

P_{\text {(odd/even) }}=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}

since both events are independent of each other.

P_{\text {(odd/even) }}=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}

Question 4 |

A solution of the following differential equation is given by \frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+6y=0

y=e^{2x}+e^{-3x} | |

y=e^{2x}+e^{3x} | |

y=e^{-2x}+e^{3x} | |

y=e^{-2x}+e^{-3x} |

Question 4 Explanation:

\begin{aligned} A E \Rightarrow\quad D^{2}-5 D+6&=0 \\ (D-2)(D-3) &=0 \\ D &=2,3 \\ \therefore \quad y &=e^{2 x}+e^{3 x} \end{aligned}

Question 5 |

The function x(t) is shown in the figure. Even and odd parts of a unit step
function u(t) are respectively,

\frac{1}{2},\frac{1}{2}x(t) | |

-\frac{1}{2},\frac{1}{2}x(t) | |

\frac{1}{2},-\frac{1}{2}x(t) | |

-\frac{1}{2},-\frac{1}{2}x(t) |

Question 5 Explanation:

\begin{array}{l} \text { Even part }=\frac{u(t)+u(-t)}{2}\\ \text { Odd part }=\frac{u(t)-u(-t)}{2} \end{array}

There are 5 questions to complete.